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SELECT `product.product_id`, `product.name`, `product.image_thumb`, `product.deleted`
FROM (`product`)
WHERE `product_id` IN (select product_id from product_category where category_id=18)
ORDER BY `display_weight` DESC

A few points:

It's possible to have a scenario where the first query will return 0 rows, but the second does contain records.

Also, you'll notice that the second query has a subquery baked in. The relationship between the product table and category table is defined in the product_category table.
The product table on its own doesn't know which categories the products belong to.